$22-$ Lucid Motors is evaluating financing options for their new automated vehicle assembly line. Three banks have provided offers, each with different interest rate structures. To make an informed decision, Lucid's finance team has been tasked with calculating the effective semiannual and effective annual interest rates for each option.

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The offers are as follows:

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a$.$ Bank A: $10\%$ per year, compounded quarterly.

b$.$ Bank B: $2\mathrm{.}5\%$ per quarter, compounded quarterly.

c$.$ Bank C: $9\mathrm{.}5\%$ per year, compounded monthly.

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$$ i$.$ What are the effective semiannual interest rates for each bank?

$$ ii$.$ What are the effective annual interest rates for each bank?

$$ iii.$$ Which bank provides the lowest effective annual interest rate?